When I typed the search into Google most of the responses were websites selling clothing and the ratio of womens versus women's was about 1:1. Searching for mens versus men's and the version with apostrophes appears almost 90% of the time. For boys versus boy's or girls versus girl's it is a 3:2 ratio in favor of no apostrophes.
So there's a general trend for leaving the apostrophe out. But "womens" looks wrong.
I suppose the same question applies to public bathrooms as well. Is the women's room or the womens room?